To further reduce the fuel consumption of internal combustion engines, and therefore to further reduce the carbon-dioxide emissions, they may be operated with oxygen excess (lean operation mode). In doing so, however, other undesirable and harmful exhaust gases such as nitrogen oxides (NOx), for example, develop. In order to treat the exhaust gases, what are termed NOx storage catalysts may be used, in which the nitrogen oxides are stored. However, since they have only a finite storage capacity, they must be emptied, i.e., regenerated regularly (e.g., in the case of motor vehicles, about every few minutes). For this purpose, the internal combustion engine is operated with a rich mixture (i.e., air deficiency) in a manner richer than stoichiometric, so that the gases of the incomplete combustion (e.g., carbon monoxide (CO) and hydrocarbons (HC)) thereby resulting are available in the NOx storage catalyst for converting the released nitrogen oxides to nitrogen.